Back in 2006, I got it into my head to try my hand at writing a simulator for the express purpose of optimizing lineups. It would go through all 9! permutations of the lineup and actually play simulated games, and then output the average runs scored for each lineup. You can see the original post here and the follow-up using stats taken from the 2005 Astros here. I never did get around to updating the algorithm (although it's still on my to-do list), but since I finally got myself a new computer I decided to try something that my friend suggested, which was to run a set of projections through the program in order to predict what the optimum lineup would be for the forthcoming year.
The program finally finished the run (marginally faster - about 50 hours run time) using the 2008 ZiPS projections for the Cubs. I used the projections for the following eight players: Lee, Ramirez, Fukudome, Soto, Pie, DeRosa, Theriot, and Soriano; and then summed up the actual 2007 lines for the five pitchers with the most ABs (Z, Lilly, Hill, Marshall, Marquis) to make a sort of "average" pitcher. I'd like to reiterate that this algorithm doesn't take into account errors, steals, player speed, GIDP, handedness, sacrifice flies or sac bunts, and baserunning is strictly station-to-station. The algorithm also does not take into account any other strategy - i.e., it doesn't pitch around guys to get to the pitcher. In addition, ZiPS doesn't project hit-by-pitches.
That said, here are the results for the top 10 and bottom 10 lineups, as well as the results for the starting lineup from the March 18th spring training game.
There is some evidence for putting your best OBP player (Fukudome) in the leadoff spot, followed by your best OPS guys with an emphasis on OBP. Unfortunately, the 2008 Cubs ZiPS projections probably aren't the best lineup for determining generalities about each lineup slot; the top 4 hitters are all within 60 points of each other in projected OPS, and the top 6 projected starters all have projected OBP within 50 points of each other as well. However, there is good support for LaRussa's "second leadoff hitter" in the 9-hole, and maybe even a "third leadoff hitter" with the pitcher in the 7th or 8th slot depending on whether your real leadoff hitter also has good pop or not. The optimum lineup here is only about 10 runs (maybe 1 win) better than the lineup Lou fielded on March 18th.